1Extension of the MDD Concept

1Extension of the MDD Concept

1.1Statistical Power

Assuming that the clothianidin coating of the OSR seeds has an effect on honey bees, statistical power is the probability that this effect is identified as a significant treatment effect using our monitoring study data. In other words, it is the probability of rejecting the null hypothesis (“there is no effect of clothianidinseed-treated OSR on honey bees”) when it is in fact false and the alternative hypothesis (“there is an effect of clothianidinseed-treated OSR on honey bees”) is true.

The power analysis conducted in this study is a method to evaluate how reliable the conclusions drawn from the hypothesis tests are. Especially, when there is no effect identified by the study results, the power analysis clarifies whether this is due to the sample size being too small or because the variance is too big. This analysis can also help answer the question whether there is a statistical non-significant but biologically significant effect or vice versa.

1.2The MDD Concept

In the aquatic mesocosm/microcosm studies, the Minimum Detectable Difference (MDD) concept was developed as an indicator of the power of a test a posteriori (Brock et al. 2014).

1.2.1For a z-Test:

•CI: Half of CI is MDD in this case!

1.2.2For a two-sample t-Test:

•Adapted from Brock et al. 2014

The MDD () is half of the confidence interval for the difference of the two group means assuming the null hypothesis is true, i.e. there is no difference between the two group means. Assuming the group mean for the reference is fixed at, then the confidence interval for the group mean of the test group should be.

1.3Generalization of MDD in the Bee Study

Although MDD is easy to obtain for mesocosm/microcosm studies, its calculation depends on the statistical analyses applied to analyze the data. In the case of the honey bee monitoring study mixed models were used. The calculation of the MDD needs to be adjusted accordingly.

A generalized linear mixed model (Bates et al. 2013, 2014) can be expressed by the following equations:

The implied marginal model is then:

Assume a general linear hypothesis of the following form is of analysis interest:

versus

The test statistic is approximately F-distributed under

Under the alternative hypothesis., the distribution of F can also be approximated by a noncentral F-distribution (Kirk, 1995).

Based on the F-distributed test statistic, the confidence interval of can be calculated and the MDD is then half of the confidence interval. However, in many instances such a linear hypothesis cannot easily be compiled because various kinds of tests were applied, including Wald-t and likelihood ratio tests, according to different scenarios. The distributions of the corresponding test statistics are often only known under the null hypothesis. In practice, extensive simulations would be required. Moreover, it is often impossible to transform the test statistic confidence intervals or critical values back to the original scale of the response variable. Hence, the MDD calculated according to the test statistic has no direct biological meaning and conveys no intuitive information on how powerful the conducted tests in the study were.

Furthermore, nonlinear relationships between the response variables and the predictors, interaction of the treatment groups, and the predictors complicate the achievement of an estimate for the treatment effect. In addition, unlike simple multiple comparisons in mesocosm/microcosm studies, multiple covariate variables were involved in our models, like day after placement (DAP), temperature sum, and humidity sum.

1.3.1Realization

A practical solution to the above problems is to calculate an MDD analogue based on the prediction confidence intervals (CIs) instead of the test statistic. The aim is to compare the reference group mean with the test group mean . The mean confidence interval bounds are based on the magnitude of the standard errors while the calculation for the test statistic for the difference between two means is based on the square root of the sum of squares of the standard errors , similar to the two-sample t-test case. Two means are statistically significantly different (with confidence level) when, that is, when the CI for the difference between the two group means does not contain zero. Two means do not have overlapping confidence intervals if , that is, if the lower bound of the CI for the greater mean (here it is assumed that is greater than ) is greater than the upper bound of the CI for the smaller mean. With some of algebraic manipulation the following can be proved:

The means are significantly different when . There is no overlap between CIs when . It is always the case that the square root of the sum of squares of two numbers is less than the sum of those numbers, i.e. . Therefore, as the difference in the means increases, it becomes significantly different before the two group mean confidence intervals cease to overlap.

The following procedure was conducted to calculate an MDD on the scale of the observed difference in response variables between the R and the T site.

1. Data augmentation.

–Use DAP as the primary predictor when it is used as a predictor in the model.

–For further covariates besides primary predictor used in the prediction model, their average (numeric covariates), most frequent value (categorical covariates), or each category (distance groups, independent sampling events) were used to obtain the predicted values.

1. Calculate estimate for both test and reference group at each assessment DAP or all DAPs as well as corresponding standard errors. The method to obtain the prediction confidence intervals and the standard errors are described in various references (Zuuret al. 2009, Bolkeret al. 2009, Bujaet al. 2009). The prediction CIs disregard the random effects from study locations and individual hives because the fixed treatment effect is of main interest. The natural variation in the bee colony development and health caused by the different locations and individual hives were captured by the random effects components in the models and were not taken into account in the determination of the treatment related effect.
2. Calculate MDD by at each DAP. It is also convenient to give the MDD as a percentage of the reference means over DAP.
3. In case of a generalized linear/additive mixed model or a transformation of the outcome variable applied before fitting the model, the MDD is calculated in the response scale by transforming the predicted mean and standard errors using the inverse link function or inverse transformation function.

The above described procedure is not restricted to any particular statistical test and is biologically meaningful. Thus, a consistent method can be used for all conducted analysis on various types of data and the power of the hypothesis testing conducted is intuitively easy to assess.

1.4References

Bates D, Maechler M, Bolker B, Walker S (2013) lme4: Linear mixed-effects models using Eigenand S4. R package version 1.1-8

Bates D, Maechler M, Bolker BM, Walker S (2015) Fitting Linear Mixed-Effects Models Using lme4. Journal of Statistical Software 67:1-48.doi:10.18637/jss.v067.i01

Bolker BM, Brooks ME, Clark CJ, Geange SW, Poulsen JR, Stevens MH, White JS (2009) Generalized linear mixed models: a practical guide for ecology and evolutionTrends EcolEvol 24:127-135

Brock TCM, Hammers-Wirtz M, Hommen U, Preuss TG, Ratte HT, Roessink I, Strauss T, and Van den Brink (2014) The minimum detectable difference (MDD) and the interpretationof treatment-related effects of pesticides in experimental ecosystems. Environ SciPollut Res Int22:1160-1174

Buja A, Cook D Hofmann H, Lawrence M, Lee EK, Swayne DF, Wickham H (2009) Statistical Inference for exploratory data analysis and model diagnostics Philos Trans A Math Phys EngSci 367:4361-4383

Kirk RE (1995) Experimental design: Procedures for the behavioral sciences. Brooks/Cole Publishing, Pacific Grove, CA

Zuur AF, Ieno EN, Walker NJ, Saveliev AA, Smith GM(2009) Mixed Effects Models andExtensions in Ecology with R.Springer Science+Business Media, New York, NY

Study location / Colony code / Hive scale / Study location / Colony code / Hive scale
1 / RA-1 / no / 3 / RA-6 / no
1 / TC-1 / no / 3 / RB-1 / no
1 / RB-6 / no / 3 / TF-1 / no
1 / RA-4 / yes / 3 / RB-4 / yes
1 / TD-6 / no / 3 / TE-3 / no
1 / RD-3 / no / 3 / TE-6 / no
1 / TF-3 / no / 3 / RA-3 / no
1 / TC-4 / yes / 3 / TF-8 / yes
1 / RE-1 / no / 3 / RE-3 / no
1 / TE-1 / no / 3 / RF-1 / no
1 / RF-6 / no / 3 / TC-3 / no
1 / RE-4 / yes / 3 / TD-4 / yes
1 / TA-1 / no / 3 / RE-6 / no
1 / TB-3 / no / 3 / TC-6 / no
1 / TB-6 / no / 3 / TD-1 / no
1 / TA-8 / yes / 3 / TB-8 / yes
1 / RD-6 / no / 3 / RC-6 / no
1 / TD-3 / no / 3 / RD-1 / no
1 / RB-3 / no / 3 / TA-3 / no
1 / RC-8 / yes / 3 / RF-4 / yes
1 / RC-1 / no / 3 / RC-3 / no
1 / RF-3 / no / 3 / TA-6 / no
1 / TF-6 / no / 3 / TB-1 / no
1 / TE-8 / yes / 3 / RD-8 / yes
2 / RA-2 / no / 4 / RA-5 / no
2 / RA-7 / no / 4 / RB-7 / no
2 / TC-2 / no / 4 / TB-2 / no
2 / TD-8 / yes / 4 / TA-4 / yes
2 / RC-2 / no / 4 / RB-2 / no
2 / TA-2 / no / 4 / TA-5 / no
2 / TA-7 / no / 4 / TB-7 / no
2 / RD-4 / yes / 4 / RC-4 / yes
2 / RE-2 / no / 4 / RE-5 / no
2 / TE-7 / no / 4 / RF-7 / no
2 / RF-5 / no / 4 / TC-5 / no
2 / RF-8 / yes / 4 / RE-8 / yes
2 / TB-5 / no / 4 / TD-2 / no
2 / TD-5 / no / 4 / RF-2 / no
2 / RC-7 / no / 4 / TD-7 / no
2 / TB-4 / yes / 4 / TE-4 / yes
2 / RB-5 / no / 4 / RC-5 / no
2 / TC-7 / no / 4 / RD-2 / no
2 / RD-5 / no / 4 / TF-7 / no
2 / RB-8 / yes / 4 / TC-8 / yes
2 / TE-2 / no / 4 / TE-5 / no
2 / RE-7 / no / 4 / TF-2 / no
2 / TF-5 / no / 4 / RD-7 / no
2 / TF-4 / yes / 4 / RA-8 / yes

TableS1Randomized assignment of honey bee hives (identified by their colony codes) to the study locations of the post-exposure phase. Hives that were placed on hive scales are indicated.

Study Location / Assessment 1 / Assessment 2 / Assessment 3 / Assessment 4
Date / DAP / Date / DAP / Date / DAP / Date / DAP
CA / 4/26/2014 / 4 / 5/3/2014 / 11 / 5/11/2014 / 19 / 5/16/2014 / 24
CB / 4/29/2014 / 7 / 5/5/2014 / 13 / 5/13/2014 / 21 / 5/18/2014 / 26
CC / 4/28/2014 / 6 / 5/4/2014 / 12 / 5/14/2014 / 22 / 5/19/2014 / 27
CD / 4/27/2014 / 5 / 5/3/2014 / 11 / 5/10/2014 / 18 / 5/16/2014 / 24
CE / 4/29/2014 / 7 / 5/5/2014 / 13 / 5/13/2014 / 21 / 5/19/2014 / 27
CF / 4/28/2014 / 6 / 5/4/2014 / 12 / 5/12/2014 / 20 / 5/17/2014 / 25
TA / 4/29/2014 / 7 / 5/5/2014 / 13 / 5/12/2014 / 20 / 5/17/2014
5/18/2014 / 25/
26
TB / 4/27/2014 / 5 / 5/3/2014 / 11 / 5/10/2014 / 18 / 5/16/2014 / 24
TC / 4/28/2014 / 6 / 5/5/2014 / 13 / 5/13/2014 / 21 / 5/19/2014 / 27
TD / 4/26/2014 / 4 / 5/3/2014 / 11 / 5/14/2014 / 22 / 5/20/2014 / 28
TE / 4/282014 / 6 / 5/4/2014 / 12 / 5/11/2014 / 19 / 5/17/2014 / 25
TF / 4/27/2014 / 5 / 5/4/2014 / 12 / 5/12/2014 / 20 / 5/18/2014 / 26

TableS2Assessment dates for individual study locations (exposure phase).

Assessment 5

Date / DAP / Colony code of assessed colonies in chronological order
6/11/2014 / 50 / RA-1, TC-1, RB-6, RA-4, RD-3, TD-6, TF-3, TC-4, RE-1, TE-1, RF-6, RE-4, RA-2, RA-7, TC-2, TD-8, RC-2, TA-2, TA-7, RD-4, RE-2, TE-7, RF-5, RF-8, TB-5, TD-5, RC-7, TB-4, RB-5, TC-7, RD-5, RB-8
6/12/2014 / 51 / TA-1, TB-3, TB-6, TA-8, RD-6, TD-3, RB-3, RC-8, RA-6, RB-1, TF-1, RB-4, TE-3, TE-6, RA-3, TF-8, RE-3, RF-1, TC-3, TD-4, RE-6, TC-6, TD-1, TB-8, RA-5, RB-7, TB-2, TA-4, RB-2, TA-5, TB-7, RC-4, RE-5, RF-7, TC-5, RE-8
6/13/2014 / 52 / RC-1, RF-3, TF-6, TE-8, RC-6, RD-1, TA-3, RF-4, RC-3, TA-6, TB-1, RD-8, TD-2, RF-2, TD-7, TE-4, RC-5, RD-2, TF-7, TC-8, TE-5, TF-2, RD-7, RA-8, TE-2, RE-7, TF-5, TF-4

Assessment 6

Date / DAP / Colony code of assessed colonies in chronological order
7/23/2014 / 92 / RA-1, TC-1, RB-6, RA-4, RA-2, RA-7, TC-2, TD-8, RC-2, RA-6, RB-1, TF-4, RB-4, RA-8, RD-7, TF-2, TE-5
7/24/2014 / 93 / TD-6, RD-3, TA-2, TA-7, RD-4, RE-2, TF-3, TC-4, TE-3, TE-6, RA-3, TF-8, RA-5, RB-7, TB-2, TA-4
7725/2014 / 94 / RE-1, TE-1, RF-6, RE-4, RB-5, TC-7, RD-5, RB-8, RC-6, RD-1, TA-3, RF-4, TD-2, RF-2, TD-7, TE-4
7/26/2014 / 95 / TA-1, TB-3, TB-6, TA-8, TE-7, RF-5, RF-8, TB-5, RE-3, TC-3, RF-1, TD-4, RB-2, TA-5, RC-4, TB-7
7/27/2014 / 96 / RD-6, TD-3, RB-3, RC-8, TD-5, RC-7, TF-1, RE-7, RE-6, TC-6, TD-1, TB-8, RE-5, RF-7, TC-5, RE-8
7/28/2014 / 97 / RC-1, RF-3, TF-6, TE-8, TE-2, TF-5, RC-3, TA-6, TB-1, RD-8, RC-5, RD-2, TF-7, TC-8

Assessment 7

Date / DAP / Colony code of assessed colonies in chronological order
9/22/2014 / 153 / TC-1, RB-6, RA-4, RD-3, TF-3, RE-1, TE-1, RF-6, RE-4, RA-7, TC-2, TD-8, RC-2, TA-2, TA-7, RD-4, RE-2, TE-7, RF-5, RF-8, RA-6, RB-1, TF-1, RB-4, TE-3, TE-6, RA-3, TF-8, RE-3, RF-1, TC-3, TD-4, RA-5, RB-7, TB-2
9/23/2014 / 154 / TA-4, RB-2, TA-5, TB-7, RC-4, RE-5, RF-7, RE-8, TD-2, RF-2, TD-7, TE-4, RC-5, RD-2, TC-8, TE-5, TF-2, RD-7, RA-8, RE-6, TC-6, TD-1, TB-8, RC-6, RD-1, TA-3, RF-4, RC-3, TA-6, TB-1, RD-8, TA-1, TB-3, TB-6, TA-8, RD-6, TD-3, RB-3, RC-8, RC-1, RF-3, TF-6, TE-8
9/24/2014 / 155 / TB-5, TD-5, RC-7, RB-5, TC-7, RD-5, TE-2, RE-7, TF-5, TF-4

TableS3Assessment dates for individual study locations (post-exposure phase).

Virus / Sequence (5’ to 3’) of forward (F) and reverse (R) primers / Annealing temperature / Length of amplicon
DWV / (F)CCTGCTAATCAACAAGGACCTGG
(R)CAGAACCAATGTCTAACGCTAACCC / 54.3°C / 355bp
SBV / (F)GTGGCAGTGTCAGATAATCC
(R)GTCAGAGAATGCGTAGTTCC / 54.3°C / 816bp
ABPV / (F)CATATTGGCGAGCCACTATG
(R)CCACTTCCACACAACTATCG / 56.8°C / 400bp
CBPV / (F)AGTTGTCATGGTTAACAGGATACGAG
(R)TCTAATCTTAGCACGAAAGCCGAG / 55.0°C / 455bp
KBV / (F) GATGAACGTCGACCTATTGA
(R)TGTGGGTTGGCTATGAGTCA / 50.5°C / 414bp

TableS4Sequences, annealing temperatures, and length of amplicons for DWV (deformed wing virus), SBV (sacbrood virus), ABPV (acute bee paralysis virus) and CBPV (chronic bee paralysis virus), KBV (Kashmir bee virus).

Step / Temperature / DWV / SBV / ABPV / CBPV / KBV
1 / 50°C / 30 min / 30 min / 30 min / 30 min / 30 min
2 / 95°C / 15 min / 15 min / 15 min / 15 min / 15 min
3 / 94°C / 1 min / 1 min / 1 min / 1 min / 1 min
4 / annealingtemperature / 1 min / 1 min / 1 min / 30 s / 1 min
5 / 72°C / 1 min / 1 min / 1 min / 1 min / 1 min
go to step 3 / × 34 / × 34 / × 36 / × 30 / × 36
6 / 72°C / 10 min / 10 min / 10 min / 10 min / 10 min
7 / 4°C / for ever / for ever / for ever / for ever / for ever

TableS5Temperature scheme for qualitative RT-PCR analysis of DWV (deformed wing virus), SBV (sacbrood virus), ABPV (acute bee paralysis virus) and CBPV (chronic bee paralysis virus) and KBV (Kashmir bee virus). For annealing temperature, see TableS4.

Study site / Assessment / DAP / Numberofbees
Mean / Standard deviation
Exposurephase / Reference / 1 / 4-7 / 12651.3 / 2554.5
Test / 1 / 4-7 / 11394.0 / 2319.9
Reference / 2 / 11-13 / 18804.8 / 4496.7
Test / 2 / 11-13 / 16311.6 / 2909.1
Reference / 3 / 18-22 / 21660.7 / 4867.2
Test / 3 / 19-22 / 20517.0 / 3086.4
Reference / 4 / 24-27 / 27761.8 / 6273.5
Test / 4 / 24-28 / 25857.6 / 4248.3
Post-exposurephase / Reference / 5 / 50-52 / 25652.7 / 7748.8
Test / 5 / 50-52 / 21978.5 / 7582.0
Reference / 6 / 92-97 / 11582.2 / 2421.0
Test / 6 / 92-97 / 10758.9 / 2752.7

TableS6Numbers of adult honey bees in study sites at different time points during the exposure phase and post-exposure phase.

Parameter / Pilling et al. 2013 / Cutler & Scott-Dupree 2007 / Cutler et al. 2014 / Rundlöfet al. 2015 / Rolkeet al. (submitted)
Current study

Experimental set-up

Substance tested / Thiamethoxam / Clothianidin (Prosper FL / Poncho 600 FS) / Clothianidin (Prosper FX) / Clothianidin (Elado) / Clothianidin (Elado)
Concentration applied / 4 g thiamethoxam/kg of seed
(plus 0.5g metalaxyl-M and 0.11g fludioxinil / kg of seed / 4g clothianidin / kg of seed
(plus fungicides thiram, carboxin, and metalaxyl) / 2.86g clothianidin / kg of seed
(plus 0.07g trifloxystrobin, 0.05g carbathiin and 0.06g metalaxyl / kg of seed) / 10g clothianidin / kg of seed
(plus 2 g β-cyfluthrin / kg of seed) / 10 g clothianidin / kg of seed
(plus 2 g β-cyfluthrin / kg of seed)
Crop / Winter oilseed rape / Spring oilseed rape / Spring oilseed rape / Spring oilseed rape / Winter oilseed rape
Seed density / 3.0-5.0 kg/ha / 8.0kg/ha / 5.6kg/ha / 7.7kg/ha / 3.4±1.1kg/ha
Location / Picardie and Alsace regions, France / Ontario, Canada / Ontario, Canada / Southern Sweden / Northern Germany
Study design/replication / Multiple exposure study (2 trials in oilseed rape; 1R field and 1T field separated by approx. 2km; approx. 2ha/field) / Four R and four T fields (ca 1ha each);
Fields at each site were separated by at least 295m / Five R and five T fields (ca 2ha each);
Fields were located a minimum of 10km apart / Replicated and matched landscapes:
eight pairs (R+T) of landscapes surrounding 16 geographically separated (>4 km) spring-sown oilseed rape fields / Two circular study sites (R+T) of ca. 65km2 each; 6locations per study site; median area of study fields: 33.5ha (9.0–97.3ha) and 5.3ha (1.22–198.0ha)
at R site and T site, respectively
Number of colonies / 6 per field (total of 24colonies) / 4 per field (total of 32colonies) / 4 per field (total of 40colonies) / 6 per field (total of 96colonies) / 8 per location (total of 96colonies)
Course of the study / 4 years / 1 season (130 days) + overwintering / 1 season + overwintering / 1 season / 1 season
Duration of exposure / 12-22 days / 21 days / 14 days / ns / 28 days
Assessment of colony strength / Liebefeld method (number of adult bees, brood area);
monitoring throughout the year and, in particular, before and after theoverwintering period / Brood assessments: approx. every 14d up to DAP98 / 7assessments + 1spring colony assessment;
digital images analyzed using digital image analysissoftware (IndiCounter® , Version 2.3) / Liebefeld method (number of adult bees only)
twice (before placement at the experimental fields, after removal fromthe experimental fields) / Liebefeld method (number of adult bees, areas of capped and open brood)
7 assessments (4 during exposure, 3 during post-exposure)
Assessment of adult mortality / Dead bee traps;
linen sheets in front of the hives / Gary dead bee traps;
white sheet placed on the ground / Drop zone dead bee trap / n.d. / Flat plastic trays covered with metal grids on the bottom board of hives

Results

Residues in honey bee pollen (T) / Alsace: 1ng/g (range: <1-1ng/g);
Picardie: <1ng/g;
(LOQ = 1ng/g) / Majority of samples below LOQ (0.5ng/g);
max.: 2.59ng/g / 0.84±0.49ng/g
max.: 1.9ng/g / 13.9±1.8ng/g (mean±SEM)
range: 6.6-23ng/g / 1st sampling: 0.50±0.30ng/g (mean±SD)
2nd sampling: 0.96±0.53ng/g (mean±SD)*
Residues in honey bee nectar (T) / Alsace: 1.7ng/g (range: <0.5-3ng/g);
Picardie: 0.7ng/g;
(LOQ = 0.5ng/g) / Majority of samples below LOQ (0.5ng/g);
max.: 2.24ng/g / below LOD (0.6ng/g) / 10.3±1.3ng/g (mean±SEM)
range: 6.7-16ng/g / 1st sampling: 0.67±0.39ng/g (mean±SD)
2nd sampling: 0.77±0.24ng/g (mean±SD)*
Residues in spring honey (T) / n.d. / Majority of samples below LOQ (0.5ng/g);
max.: 0.93ng/g / below LOD (0.6ng/g) / n.d. / 1.35±0.48ng/g*
Percentage of OSR pollen in bee-collected pollen / n.d. / n.d. / R: 84.9±15.2%
T: 91.0±6.2% / 57.8±5.0% (similar proportions for R and T) / 1stsampling:
R: 32.3%±21.2%
T: 35.8%±13.5%;
2ndsampling:
R: 77.5%±14.1%
T: 82.8%±8.8%
Colony strength / no effect / no effect / no effect / no effect / no effect
Number of capped brood cells / no effect / no effect / no effect / n.d. / no effect
Hive weight gain / no effect / no effect / no effect / n.d. / no effect
Honey yield / n.d. / no effect / no effect / n.d. / no effect
Pests and diseases / n.d. / n.d. / no effect
(Varroa, Nosema, AFB, EFB, chalkbrood, tracheal mite) / n.d. / no effect
(Varroa, Nosema, DWV, SBV, ABPV, CBPV, KBV)
Bee mortality / no effect / no effect / no effect / n.d. / no effect
Overwintering survival/Spring colony assessment / no effect / no effect / no effect / n.d. / n.d.

Table S7Comparison of five monitoring/field studies on the effects of neonicotinoid seed-treated oilseed rape on the performance of honey bee colonies regarding experimental set-up and outcome. Abbreviations: ABPV, acute bee paralysis virus; AFB, American foulbrood; CBV, chronic bee paralysis virus; DAP, day after placement; DWV, deformed wing virus; EFB, European foulbrood; KBV, Kashmir bee virus; LOD, limit of detection; LOQ, limit of quantification; n.d., not determined; ns, not specified; OSR, oilseed rape; SBV, R, reference; sacbrood virus; T, test. * data from Rolkeet al. (submitted, this issue).

Fig.S1:Study locations and arrangement of honey bee hives during the post-exposure phase. A: Study locations (red points) during post-exposure phase. B: Arrangement of honey bee hives at the study locations during the post-exposure phase. a = honey bee hive, b = honey bee hive on a balance, c = honey bee hive on a balance connected to a rain gauge, d = anemometer.

Fig.S2:Daily fall of dead bees in colonies located at study locations in the reference site and the test site.The box plots contain the 1st and 3rd quartiles, split by the median; traditional Tukey whiskers go 1.5 times the interquartile distance or to the highest or lowest point, whichever is shorter.Any data beyond these whiskers are shown as points.DAP, day after placement.

Fig.S2Naturally occurring (A) and flumethrin-induced (B) daily Varroa destructor mite fall in colonies located at study locations in the reference site and the test site. Dots indicate outliers.